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Mat. Sb., 2003, Volume 194, Number 12, Pages 31–62 (Mi msb786)  

This article is cited in 4 scientific papers (total in 4 papers)

Beta functions of Bruhat–Tits buildings and deformation of $l^2$ on the set of $p$-adic lattices

Yu. A. Neretin

Institute for Theoretical and Experimental Physics (Russian Federation State Scientific Center)

Abstract: For the space $\operatorname{Lat}_n$ of all lattices in an $n$-dimensional $p$-adic linear space an analogue of the matrix beta function is constructed; this beta function can degenerate to the Tamagawa zeta function. An analogue of Berezin kernels for $\operatorname{Lat}_n$ is proposed. Conditions for the positive-definiteness of these kernels and an explicit Plancherel's formula are obtained.

DOI: https://doi.org/10.4213/sm786

Full text: PDF file (465 kB)
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English version:
Sbornik: Mathematics, 2003, 194:12, 1775–1805

Bibliographic databases:

UDC: 519.46
MSC: 20E42, 37A45, 53C35
Received: 12.05.2003

Citation: Yu. A. Neretin, “Beta functions of Bruhat–Tits buildings and deformation of $l^2$ on the set of $p$-adic lattices”, Mat. Sb., 194:12 (2003), 31–62; Sb. Math., 194:12 (2003), 1775–1805

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Yu. A. Neretin, “On compression of Bruhat–Tits buildings”, J. Math. Sci. (N. Y.), 138:3 (2006), 5722–5726  mathnet  crossref  mathscinet  zmath  elib  elib
    2. J. Math. Sci. (N. Y.), 141:4 (2007), 1452–1478  mathnet  crossref  mathscinet  zmath  elib
    3. Ji Lizhen, “Buildings and their application in geometry and topology”, Asian J. Math., 10:1 (2006), 11–80  crossref  mathscinet  zmath  isi  scopus
    4. Yu. A. Neretin, “Hua measures on the space of $p$-adic matrices and inverse limits of Grassmannians”, Izv. Math., 77:5 (2013), 941–953  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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